共查询到20条相似文献,搜索用时 0 毫秒
1.
This paper examines the properties of a fractional diffusion equation
defined by the composition of the inverses of the Riesz potential and the
Bessel potential. The first part determines the conditions under which the
Green function of this equation is the transition probability density
function of a Lévy motion. This Lévy motion is obtained by the
subordination of Brownian motion, and the Lévy representation of the
subordinator is determined. The second part studies the semigroup formed by
the Green function of the fractional diffusion equation. Applications of
these results to certain evolution equations is considered. Some results on
the numerical solution of the fractional diffusion equation are also
provided. 相似文献
2.
Explicit inversion formulas of Balakrishnan–Rubin type and a characterization of Bessel potentials associated with the Laplace–Bessel differential operator
are obtained. As an auxiliary tool the B-metaharmonic semigroup is introduced and some of its properties are investigated. 相似文献
4.
§1. IntroductionNowadays,theresearchoftheinfintedelayfunctionaldifferentialquationhasdevelopeddeeply.Manyliteratureshavebeenconcernedforresearchtheintegraldifferentialquationasfollowsx(t)=-a(t)x(t)+∫t-∞k(t,s-t,x(s))ds.(1) Inordertostudytheinfinited… 相似文献
5.
TheAsymptoticsStabilityofSolutionsofSome FourthOrderDifferentialEquation方欣华TheAsymptoticsStabilityofSolutionsofSomeFourthOrde... 相似文献
6.
By using some differential inequality, a second-order delay differential equation(r(t)x′(t))′ p(t)x(q(t)) = 0has been investigated and some necessary condition for this equation has a nonoscillatorysolution and some sufficient condition which ensures that all of the solutions of the aboveequation are oscillatory are obtained. 相似文献
7.
We study the second boundary-value problem in a half-strip for a differential equation with Bessel operator and the Riemann–Liouville partial derivative. In the case of a zero initial condition, a representation of the solution is obtained in terms of the Fox H-function. The uniqueness of the solution is proved for the class of functions satisfying an analog of the Tikhonov condition. 相似文献
9.
In this note, a theorem and its three corollaries on solution of the first order ordinary differential equation are given. Theorem Suppose that b, F∈C,a∈C~1,b(y)≠0. If a(t) and b(t) satisfy the equality a′(t)b(t)=1, (1) then the first order differential equation y′=b(y)F(x,a(y)) (2) has a solution y=f(u) (3) where u=u(x) is a solution of the equatien 相似文献
10.
In this paper, we study necessary conditions for the existence and uniqueness of continuous solution for a nonlocal boundary value problem with nonlinear term involving Riemann–Liouville fractional derivative. Our results are based on Schauder fixed point theorem and the Banach contraction principle fixed point theorem. Examples illustrating the obtained results are also presented. 相似文献
11.
We prove that a deformation of a hypersurface in an ( n + 1)-dimensional real space form \({{\mathbb S}^{n+1}_{p,1}}\) induces a Hamiltonian variation of the normal congruence in the space \({{\mathbb L}({\mathbb S}^{n+1}_{p,1})}\) of oriented geodesics. As an application, we show that every Hamiltonian minimal submanifold in \({{\mathbb L}({\mathbb S}^{n+1})}\) (resp. \({{\mathbb L}({\mathbb H}^{n+1})}\)) with respect to the (para-)Kähler Einstein structure is locally the normal congruence of a hypersurface \({\Sigma}\) in \({{\mathbb S}^{n+1}}\) (resp. \({{\mathbb H}^{n+1}}\)) that is a critical point of the functional \({{\mathcal W}(\Sigma) = \int_\Sigma\left(\Pi_{i=1}^n|\epsilon+k_i^2|\right)^{1/2}}\), where ki denote the principal curvatures of \({\Sigma}\) and \({\epsilon \in \{-1, 1\}}\). In addition, for \({n = 2}\), we prove that every Hamiltonian minimal surface in \({{\mathbb L}({\mathbb S}^{3})}\) (resp. \({{\mathbb L}({\mathbb H}^{3})}\)), with respect to the (para-)Kähler conformally flat structure, is the normal congruence of a surface in \({{\mathbb S}^{3}}\) (resp. \({{\mathbb H}^{3}}\)) that is a critical point of the functional \({{\mathcal W}\prime(\Sigma) = \int_\Sigma\sqrt{H^2-K+1}}\) (resp. \({{\mathcal W}\prime(\Sigma) = \int_\Sigma\sqrt{H^2-K-1}}\)), where H and K denote, respectively, the mean and Gaussian curvature of \({\Sigma}\). 相似文献
12.
Lyapunov's second method in fact is that which may be described as follows:applying the comparison principle to the V-function, we may render the stability ofthe solution of a vector differential.equation to that of the scalar differential equation du/dt=ω(t,u),ω(t,0)≡0,0≤u≤ρ(t),t∈ [cf. C. Corduneanu, 1960]. Unfortunately, the stability of the solutions of scalardifferential equations had not been well-discussed. In literatures, ρ is assumed to be 相似文献
13.
We prove local well-posedness of the initial-boundary value problem for the Korteweg–de Vries equation on right half-line, left half-line, and line segment, in the low regularity setting. This is accomplished by introducing an analytic family of boundary forcing operators. 相似文献
14.
We discuss the existence and the number of periodic solutions of differential equation dx/dt=A1(t)x A2(t)x^2 A3(t)x^3/α0(t) α1(t)x α2(t)x^2 (1)where Ai(t),αj(t)(i=1,2,3;j=0,1,2) are continuous periodic functions.The results of this paper ex-tend the work of paper[1]. 相似文献
15.
In this work, we study a class of nonlocal neutral fractional differential equations with deviated argument in the separable Hilbert space. We obtain an associated integral equation and then, consider a sequence of approximate integral equations. We investigate the existence and uniqueness of the mild solution for every approximate integral equation by virtue of the theory of analytic semigroup theory via the technique of Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. The Faedo–Galerkin approximation of the solution is studied and demonstrated some convergence results. Finally, we give an example. 相似文献
16.
PeriodicSolutionofNonlinearParabolicDifferentialEquationWithTimeLag¥(王克)WangKe(DepartmentofMathematics,NortheastNormalUnivers... 相似文献
17.
AbstractIn this article, we investigate Lie bialgebra structures on the deformed twisted Heisenberg–Virasoro Lie algebra. Sufficient and necessary conditions for this type Lie bialgebra structures to be triangular coboundary are given.Communicated by K. C. Misra 相似文献
19.
Archiv der Mathematik - We prove an identity that implies the classical Rellich inequality as well as several improved versions of Rellich type inequalities. Moreover, our equality gives a simple... 相似文献
20.
This work deals with the convergence and stability of Runge–Kutta methods for systems of differential equation with piecewise continuous arguments x′( t) = Px( t)+ Qx([ t+1∕2]) under two cases for coe?cient matrix. First, when P and Q are complex matrices, the su?cient condition under which the analytic solution is asymptotically stable is given. It is proven that the Runge–Kutta methods are convergent with order p. Moreover, the su?cient condition under which the analytical stability region is contained in the numerical stability region is obtained. Second, when P and Q are commutable Hermitian matrices, using the theory of characteristic, the necessary and su?cient conditions under which the analytic solution and the numerical solution are asymptotically stable are presented, respectively. Furthermore, whether the Runge–Kutta methods preserve the stability of analytic solution are investigated by the theory of Padé approximation and order star. To demonstrate the theoretical results, some numerical experiments are adopted. 相似文献
|